Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
 
 
public class Main{

   public static void main(String[] args) throws IOException{
	
	int t = sc.nextInt();
	out.println(t/2+1);
	for (int i = 1; i <= t/2+1; i++) {
		out.println("1 " + i);
	}
	
	int count = t/2+2;
	for (int i = 2; count <= t; i++) {
		out.println(i + " " + (t/2+1));
		count++;
	}
	
	out.close();
   }
   
  

   
   
   static class Reader 
   { 
       final private int BUFFER_SIZE = 1 << 16; 
       private DataInputStream din; 
       private byte[] buffer; 
       private int bufferPointer, bytesRead; 

       public Reader() 
       { 
           din = new DataInputStream(System.in); 
           buffer = new byte[BUFFER_SIZE]; 
           bufferPointer = bytesRead = 0; 
       } 

       public Reader(String file_name) throws IOException 
       { 
           din = new DataInputStream(new FileInputStream(file_name)); 
           buffer = new byte[BUFFER_SIZE]; 
           bufferPointer = bytesRead = 0; 
       } 

       public String readLine() throws IOException 
       { 
           byte[] buf = new byte[64]; // line length 
           int cnt = 0, c; 
           while ((c = read()) != -1) 
           { 
               if (c == '\n') 
                   break; 
               buf[cnt++] = (byte) c; 
           } 
           return new String(buf, 0, cnt); 
       } 

       public int nextInt() throws IOException 
       { 
           int ret = 0; 
           byte c = read(); 
           while (c <= ' ') 
               c = read(); 
           boolean neg = (c == '-'); 
           if (neg) 
               c = read(); 
           do
           { 
               ret = ret * 10 + c - '0'; 
           }  while ((c = read()) >= '0' && c <= '9'); 

           if (neg) 
               return -ret; 
           return ret; 
       } 

       public long nextLong() throws IOException 
       { 
           long ret = 0; 
           byte c = read(); 
           while (c <= ' ') 
               c = read(); 
           boolean neg = (c == '-'); 
           if (neg) 
               c = read(); 
           do { 
               ret = ret * 10 + c - '0'; 
           } 
           while ((c = read()) >= '0' && c <= '9'); 
           if (neg) 
               return -ret; 
           return ret; 
       } 

       public double nextDouble() throws IOException 
       { 
           double ret = 0, div = 1; 
           byte c = read(); 
           while (c <= ' ') 
               c = read(); 
           boolean neg = (c == '-'); 
           if (neg) 
               c = read(); 

           do { 
               ret = ret * 10 + c - '0'; 
           } 
           while ((c = read()) >= '0' && c <= '9'); 

           if (c == '.') 
           { 
               while ((c = read()) >= '0' && c <= '9') 
               { 
                   ret += (c - '0') / (div *= 10); 
               } 
           } 

           if (neg) 
               return -ret; 
           return ret; 
       } 

       private void fillBuffer() throws IOException 
       { 
           bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
           if (bytesRead == -1) 
               buffer[0] = -1; 
       } 

       private byte read() throws IOException 
       { 
           if (bufferPointer == bytesRead) 
               fillBuffer(); 
           return buffer[bufferPointer++]; 
       } 

       public void close() throws IOException 
       { 
           if (din == null) 
               return; 
           din.close(); 
       } 
   }

	public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
	public static Reader sc = new Reader();
}